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FFTW FAQ - Section 3
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FFTW FAQ - Section 3 <br>
Using FFTW
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<ul>
<li><a href="#fftw2to3" rel=subdocument>Q3.1. Why not support the FFTW 2 interface in FFTW
3?</a>
<li><a href="#planperarray" rel=subdocument>Q3.2. Why do FFTW 3 plans encapsulate the input/output arrays and not just
the algorithm?</a>
<li><a href="#slow" rel=subdocument>Q3.3. FFTW seems really slow.</a>
<li><a href="#slows" rel=subdocument>Q3.4. FFTW slows down after repeated calls.</a>
<li><a href="#segfault" rel=subdocument>Q3.5. An FFTW routine is crashing when I call it.</a>
<li><a href="#fortran64" rel=subdocument>Q3.6. My Fortran program crashes when calling FFTW.</a>
<li><a href="#conventions" rel=subdocument>Q3.7. FFTW gives results different from my old
FFT.</a>
<li><a href="#nondeterministic" rel=subdocument>Q3.8. FFTW gives different results between runs</a>
<li><a href="#savePlans" rel=subdocument>Q3.9. Can I save FFTW's plans?</a>
<li><a href="#whyscaled" rel=subdocument>Q3.10. Why does your inverse transform return a scaled
result?</a>
<li><a href="#centerorigin" rel=subdocument>Q3.11. How can I make FFTW put the origin (zero frequency) at the center of
its output?</a>
<li><a href="#imageaudio" rel=subdocument>Q3.12. How do I FFT an image/audio file in <i>foobar</i> format?</a>
<li><a href="#linkfails" rel=subdocument>Q3.13. My program does not link (on Unix).</a>
<li><a href="#linkheader" rel=subdocument>Q3.14. I included your header, but linking still
fails.</a>
<li><a href="#nostack" rel=subdocument>Q3.15. My program crashes, complaining about stack
space.</a>
<li><a href="#leaks" rel=subdocument>Q3.16. FFTW seems to have a memory leak.</a>
<li><a href="#allzero" rel=subdocument>Q3.17. The output of FFTW's transform is all zeros.</a>
<li><a href="#vbetalia" rel=subdocument>Q3.18. How do I call FFTW from the Microsoft language du
jour?</a>
<li><a href="#pruned" rel=subdocument>Q3.19. Can I compute only a subset of the DFT outputs?</a>
<li><a href="#transpose" rel=subdocument>Q3.20. Can I use FFTW's routines for in-place and out-of-place matrix
transposition?</a>
</ul><hr>

<h2><A name="fftw2to3">
Question 3.1.  Why not support the FFTW 2 interface in FFTW
3?
</A></h2>

FFTW 3 has semantics incompatible with earlier versions: its plans can
only be used for a given stride, multiplicity, and other
characteristics of the input and output arrays; these stronger
semantics are necessary for performance reasons.  Thus, it is
impossible to efficiently emulate the older interface (whose plans can
be used for any transform of the same size).  We believe that it
should be possible to upgrade most programs without any difficulty,
however.  
<h2><A name="planperarray">
Question 3.2.  Why do FFTW 3 plans encapsulate the input/output arrays
and not just the algorithm?
</A></h2>

There are several reasons: 
<ul>
<li>It was important for performance reasons that the plan be specific to
array characteristics like the stride (and alignment, for SIMD), and
requiring that the user maintain these invariants is error prone. 

<li>In most high-performance applications, as far as we can tell, you are
usually transforming the same array over and over, so FFTW's semantics
should not be a burden.  
<li>If you need to transform another array of the same size, creating a
new plan once the first exists is a cheap operation. 

<li>If you need to transform many arrays of the same size at once, you
should really use the <code>plan_many</code> routines in FFTW's &quot;advanced&quot;
interface.  
<li>If the abovementioned array characteristics are the same, you are
willing to pay close attention to the documentation, and you really
need to, we provide a &quot;new-array execution&quot; interface to
apply a plan to a new array.  
</ul>

<h2><A name="slow">
Question 3.3.  FFTW seems really slow.
</A></h2>

You are probably recreating the plan before every transform, rather
than creating it once and reusing it for all transforms of the same
size.  FFTW is designed to be used in the following way:

<ul>
<li>First, you create a plan.  This will take several seconds. 

<li>Then, you reuse the plan many times to perform FFTs.  These are fast. 

</ul>
If you don't need to compute many transforms and the time for the
planner is significant, you have two options.  First, you can use the
<code>FFTW_ESTIMATE</code> option in the planner, which uses heuristics
instead of runtime measurements and produces a good plan in a short
time.  Second, you can use the wisdom feature to precompute the plan;
see <A href="#savePlans">Q3.9 `Can I save FFTW's plans?'</A> 
<h2><A name="slows">
Question 3.4.  FFTW slows down after repeated
calls.
</A></h2>

Probably, NaNs or similar are creeping into your data, and the
slowdown is due to the resulting floating-point exceptions.  For
example, be aware that repeatedly FFTing the same array is a diverging
process (because FFTW computes the unnormalized transform). 

<h2><A name="segfault">
Question 3.5.  An FFTW routine is crashing when I call
it.
</A></h2>

Did the FFTW test programs pass (<code>make check</code>, or <code>cd tests; make bigcheck</code> if you want to be paranoid)?  If so, you almost
certainly have a bug in your own code.  For example, you could be
passing invalid arguments (such as wrongly-sized arrays) to FFTW, or
you could simply have memory corruption elsewhere in your program that
causes random crashes later on.  Please don't complain to us unless
you can come up with a minimal self-contained program (preferably
under 30 lines) that illustrates the problem. 

<h2><A name="fortran64">
Question 3.6.  My Fortran program crashes when calling
FFTW.
</A></h2>

As described in the manual, on 64-bit machines you must store the
plans in variables large enough to hold a pointer, for example
<code>integer*8</code>.  We recommend using <code>integer*8</code> on 32-bit machines as well, to simplify porting. 

<h2><A name="conventions">
Question 3.7.  FFTW gives results different from my old
FFT.
</A></h2>

People follow many different conventions for the DFT, and you should
be sure to know the ones that we use (described in the FFTW manual). 
In particular, you should be aware that the
<code>FFTW_FORWARD</code>/<code>FFTW_BACKWARD</code> directions correspond to signs of -1/+1 in the exponent of the DFT definition. 
(<i>Numerical Recipes</i> uses the opposite convention.)   
<p>
You should also know that we compute an unnormalized transform.  In
contrast, Matlab is an example of program that computes a normalized
transform.  See <A href="#whyscaled">Q3.10 `Why does your inverse transform return a scaled
result?'</A>.  
<p>
Finally, note that floating-point arithmetic is not exact, so
different FFT algorithms will give slightly different results (on the
order of the numerical accuracy; typically a fractional difference of
1e-15 or so in double precision).  
<h2><A name="nondeterministic">
Question 3.8.  FFTW gives different results between
runs
</A></h2>

If you use <code>FFTW_MEASURE</code> or <code>FFTW_PATIENT</code> mode, then the algorithm FFTW employs is not deterministic: it depends on
runtime performance measurements.  This will cause the results to vary
slightly from run to run.  However, the differences should be slight,
on the order of the floating-point precision, and therefore should
have no practical impact on most applications. 

<p>
If you use saved plans (wisdom) or <code>FFTW_ESTIMATE</code> mode, however, then the algorithm is deterministic and the results should be
identical between runs.  
<h2><A name="savePlans">
Question 3.9.  Can I save FFTW's plans?
</A></h2>

Yes. Starting with version 1.2, FFTW provides the
<code>wisdom</code> mechanism for saving plans; see the FFTW manual. 

<h2><A name="whyscaled">
Question 3.10.  Why does your inverse transform return a scaled
result?
</A></h2>

Computing the forward transform followed by the backward transform (or
vice versa) yields the original array scaled by the size of the array.
 (For multi-dimensional transforms, the size of the array is the
product of the dimensions.)  We could, instead, have chosen a
normalization that would have returned the unscaled array. Or, to
accomodate the many conventions in this matter, the transform routines
could have accepted a &quot;scale factor&quot; parameter. We did not
do this, however, for two reasons. First, we didn't want to sacrifice
performance in the common case where the scale factor is 1. Second, in
real applications the FFT is followed or preceded by some computation
on the data, into which the scale factor can typically be absorbed at
little or no cost.  
<h2><A name="centerorigin">
Question 3.11.  How can I make FFTW put the origin (zero frequency) at
the center of its output?
</A></h2>

For human viewing of a spectrum, it is often convenient to put the
origin in frequency space at the center of the output array, rather
than in the zero-th element (the default in FFTW).  If all of the
dimensions of your array are even, you can accomplish this by simply
multiplying each element of the input array by (-1)^(i + j + ...),
where i, j, etcetera are the indices of the element.  (This trick is a
general property of the DFT, and is not specific to FFTW.)

<h2><A name="imageaudio">
Question 3.12.  How do I FFT an image/audio file in
<i>foobar</i> format?
</A></h2>

FFTW performs an FFT on an array of floating-point values.  You can
certainly use it to compute the transform of an image or audio stream,
but you are responsible for figuring out your data format and
converting it to the form FFTW requires. 

<h2><A name="linkfails">
Question 3.13.  My program does not link (on
Unix).
</A></h2>

The libraries must be listed in the correct order
(<code>-lfftw3 -lm</code> for FFTW 3.x) and <i>after</i> your program sources/objects.  (The general rule is that if <i>A</i> uses <i>B</i>, then <i>A</i> must be listed before <i>B</i> in the link command.).  
<h2><A name="linkheader">
Question 3.14.  I included your header, but linking still
fails.
</A></h2>

You're a C++ programmer, aren't you?  You have to compile the FFTW
library and link it into your program, not just
<code>#include &lt;fftw3.h&gt;</code>.  (Yes, this is really a FAQ.) 
<h2><A name="nostack">
Question 3.15.  My program crashes, complaining about stack
space.
</A></h2>

You cannot declare large arrays with automatic storage (e.g. via
<code>fftw_complex array[N]</code>); you should use <code>fftw_malloc</code> (or equivalent) to allocate the arrays you want
to transform if they are larger than a few hundred elements. 

<h2><A name="leaks">
Question 3.16.  FFTW seems to have a memory
leak.
</A></h2>

After you create a plan, FFTW caches the information required to
quickly recreate the plan.  (See <A href="#savePlans">Q3.9 `Can I save FFTW's plans?'</A>) It also maintains a small amount of other persistent memory.  You can deallocate all of
FFTW's internally allocated memory, if you wish, by calling
<code>fftw_cleanup()</code>, as documented in the manual.  
<h2><A name="allzero">
Question 3.17.  The output of FFTW's transform is all
zeros.
</A></h2>

You should initialize your input array <i>after</i> creating the plan, unless you use <code>FFTW_ESTIMATE</code>: planning with <code>FFTW_MEASURE</code> or <code>FFTW_PATIENT</code> overwrites the input/output arrays, as described in the manual. 

<h2><A name="vbetalia">
Question 3.18.  How do I call FFTW from the Microsoft language du
jour?
</A></h2>

Please <i>do not</i> ask us Windows-specific questions.  We do not
use Windows.  We know nothing about Visual Basic, Visual C++, or .NET.
 Please find the appropriate Usenet discussion group and ask your
question there.  See also <A href="section2.html#runOnWindows">Q2.2 `Does FFTW run on Windows?'</A>.  
<h2><A name="pruned">
Question 3.19.  Can I compute only a subset of the DFT
outputs?
</A></h2>

In general, no, an FFT intrinsically computes all outputs from all
inputs.  In principle, there is something called a
<i>pruned FFT</i> that can do what you want, but to compute K outputs out of N the
complexity is in general O(N log K) instead of O(N log N), thus saving
only a small additive factor in the log.  (The same argument holds if
you instead have only K nonzero inputs.)

<p>
There are some specific cases in which you can get the O(N log K)
performance benefits easily, however, by combining a few ordinary
FFTs.  In particular, the case where you want the first K outputs,
where K divides N, can be handled by performing N/K transforms of size
K and then summing the outputs multiplied by appropriate phase
factors.  For more details, see <A href="http://www.fftw.org/pruned.html">pruned FFTs with FFTW</A>.  
<p>
There are also some algorithms that compute pruned transforms
<i>approximately</i>, but they are beyond the scope of this FAQ. 

<h2><A name="transpose">
Question 3.20.  Can I use FFTW's routines for in-place and
out-of-place matrix transposition?
</A></h2>

You can use the FFTW guru interface to create a rank-0 transform of
vector rank 2 where the vector strides are transposed.  (A rank-0
transform is equivalent to a 1D transform of size 1, which.  just
copies the input into the output.)  Specifying the same location for
the input and output makes the transpose in-place. 

<p>
For double-valued data stored in row-major format, plan creation looks
like this: <pre>
fftw_plan plan_transpose(int rows, int cols, double *in, double *out)
{
    const unsigned flags = FFTW_ESTIMATE; /* other flags are possible */
    fftw_iodim howmany_dims[2];

    howmany_dims[0].n  = rows;
    howmany_dims[0].is = cols;
    howmany_dims[0].os = 1;

    howmany_dims[1].n  = cols;
    howmany_dims[1].is = 1;
    howmany_dims[1].os = rows;

    return fftw_plan_guru_r2r(/*rank=*/ 0, /*dims=*/ NULL,
                              /*howmany_rank=*/ 2, howmany_dims,
                              in, out, /*kind=*/ NULL, flags);
}
</pre>
(This entry was written by Rhys Ulerich.)
<hr>
Next: <a href="section4.html" rel=precedes>Internals of FFTW</a>.<br>
Back: <a href="section2.html" rev=precedes>Installing FFTW</a>.<br>
<a href="index.html" rev=subdocument>Return to contents</a>.<p>
<address>
<A href="http://www.fftw.org">Matteo Frigo and Steven G. Johnson</A> / <A href="mailto:fftw@fftw.org">fftw@fftw.org</A>
- 14 September 2021
</address><br>
Extracted from FFTW Frequently Asked Questions with Answers,
Copyright &copy; 2021 Matteo Frigo and Massachusetts Institute of Technology.
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